The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That is, bidding your true value is a weakly dominant strategy in SPA, whereas in FPA, bidding below your true value is the dominant strategy. See this question.

My question is: why does it matter to the seller whether people bid truthfully or not? Initially, I thought that since SPA induce truthful bidding, they also maximize expected revenue for the seller, which is why a seller would use SPA. But, according to the revenue equivalence theorem, FPA and SPA generate the same expected revenue. So, shouldn't it not matter to the seller what auction they choose? Why would a seller prefer SPA -- which are generally harder to explain -- if it doesn't generate higher expected revenue?

I can think of three possible explanations:

  1. There's a mismatch between theory and the real world. Maybe in theory SPA and FPA should generate the same revenue, but in practice they don't. If so, is there any empirical research that shows this?
  2. The seller's goal is to collect information rather than to maximize revenue. Maybe the seller has a product and they don't know how much to sell it for. In that case, an SPA could help them generate an accurate demand curve.
  3. To benefit the buyer. If there's no cost to the seller in terms of revenue, but a benefit to the buyer, a seller might want to use SPA. But this leads to the question: why does the seller care about helping the buyer? Maybe in order to encourage more buyers to participate in the auction? And, possibly encouraging more buyers to enter the auction would raise the expected revenue from the auction, if those new buyers were higher bidders.

Since SPA are so common in online advertising (google adwords) and eBay, they might be the most widely used auction there is today. So, I'm wondering why sellers prefer them to FPA. Is any of these explanations on the right track?

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    $\begingroup$ Just as a side note- there are variations of Second Price Auctions that are just as easy (if not easier) to understand than FPAs. One example is an English (ascending price) auction, which effectively mimics a SPA. In that case, you pay the lowest bid that's higher than all other bidders' valuations- not your own true valuation of a good. I mention it just as a case where it's important to keep in mind the broadest scope of what SPAs actually observe and how they operate. $\endgroup$ – AndrewC Sep 5 '18 at 0:43

I don't think sellers would prefer SPA over FPA. In fact, the SPA is riskier than the FPA, if we look at it from a seller's perspective. The reason is because the distribution of prices in case of the SPA is a mean preserving spread of the distribution of prices in FPA(you can refer to Vijay Krishna's Auction Theory for the proof).

However, the VCG mechanism finds a lot of applications in real life scenarios(like in case of network routing algorithms). It just so happens that the VCG mechanism can turn out to be the second price auction, given that certain conditions are met.

The Generalized SPA is another such example, that draws its basis from the standard SPA. Please see https://en.wikipedia.org/wiki/Generalized_second-price_auction .

As far as the English Auction is considered, it is equivalent to the SPA only in the case of independent bidders. If the values realized by the bidders depend upon the the values realized by others(meaning the valuations are now interdependent), the English Auction no longer remains equivalent to the SPA(interdependence is something that on can expect to be more prevalent in real life cases).

Another thing, the RET states that the 'expected revenue' is same for standard auctions with symmetric bidders. The payment received by the seller is just the highest bid. Thus, receiving a higher payment in either auction(FPA or SPA) depends on the values realized by the bidders(and the bidding strategy).

  • $\begingroup$ Interesting! I didn't know that SPA were mean-preserving spreads of FPA; thanks for the citation. I think I'm still confused though. If SPA are not necessarily better for the seller - and if sellers don't even necessarily prefer them - then why are they so widely used by sellers? It makes sense that SPA might be used just because it's an application of the VCG mechanism. But isn't the benefit of a VCG mechanism that it produces a socially optimal result? In that case, why does the seller care about producing a socially optimal result, as opposed to just a results that's optimal for them? 1/2 $\endgroup$ – Steve Sep 7 '18 at 19:12
  • $\begingroup$ One guess is that it's not necessarily the sellers that are choosing to use SPA/VCG, it's the platforms they sell things on (google adwords, eBay, etc); and these platforms are concerned with producing socially optimal results, so the sellers go along with it? if it is true, though, that SPA are riskier to sellers, i'd still probably expect them to be less dominant in the ad selling industry. 2/2 $\endgroup$ – Steve Sep 7 '18 at 19:12

I would argue that the principal benefit to the (simple) second-price (or Vickrey) auction is the fact that it is easy. That is, it is weakly dominant strategy simply just to bid your own valuation. Straightforward. As Vickrey (1961) writes,

"Each bidder can confine his efforts and attention to an appraisal of the value the article would have in his own hands, at a considerable saving in mental strain and possibly in out-of-pocket expense."

See the recent paper, "Obviously Strategy-Proof Mechanisms" (Li 2017 AER) for further discussion related to this post


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    $\begingroup$ Ah I see. I was thinking SPA are more difficult since they're less familiar and thus harder to explain to people. But you're saying SPA are easy in the sense that they require less mental strain on the bidder, since they're strategy-proof. I think this still raises the question of why a seller would care about this. Is it because making the buyer more happy/comfortable will induce more bidders to bid? $\endgroup$ – Steve Sep 7 '18 at 18:56
  • $\begingroup$ @Steve right. I think it relates to the "realism" of the model, especially since the topic is auction design, which is perhaps the most real-world relevant (at least in the sense of having direct effect on firms) of topics in micro theory. Requiring people to carry out sophisticated strategies might not be terribly plausible. Your statement suggests a nice model--extend Li's paper to include endogenous participation contingent on the complexity of the auction. $\endgroup$ – user11305 Sep 7 '18 at 23:28
  • $\begingroup$ Interestingly, in another paper by the same author (along with M. Akbarpour (spelling?)), an argument is forwarded which says essentially that, "hang on, the reason why we might not see 2nd price auctions that often is because it's hard to detect funny business on the part of the auctioneer". $\endgroup$ – user11305 Sep 7 '18 at 23:28
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    $\begingroup$ That paper is "Credible Mechanisms". $\endgroup$ – user11305 Sep 7 '18 at 23:29

The SPA/VCG rule has not only the characteristics other have mentioned here - namely that truthful reporting your valuation is weakly dominant. There's an important feature of it that more often than not goes unmentioned.

So, what exactly is the SPA/Vickrey Auction? The Vickrey-Clarke-Groves mechanism is basically a pair of primal-dual linear programming problems. The primal's solution gives us who should get the good and the dual's solution, how much is this agent supposed to pay. This is isn't accidental. It resembles perfect competition general equilibrium models, which one can describe as linear programming problems in finite dimension.

In pigouvian terms, the VCG mechanism guarantees there's no mismatch between social and private marginal gains. There's a deep price theory implication in the VCG mechanism.

As Ostroy showed in 1980, perfect competition implies alignment between private benefits and each agent's social shadow-price. This also happens in a Vickrey Auction. As a matter of fact, one can think of a perfectly competitive market as a giant Vickrey Auction.

Second price/ Vickrey auctions mirror perfect competition. That's why they're vastly preferred. Expected revenue may be the same, but allocative efficiency is definitely better.


I think an argument for why seller care about SPA is that by making the mechanism strategy proof, it would increase efficiency for the bidders so that a large amount of items can be sold in a short amount of time. (e.g. ad on search engines, google probably does not want to deal with ppl trying to strategize, attempt to gain info about competitor, etc etc.)

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    $\begingroup$ Google ad auctions are not single unit auctions. First, second and third placement for a single keyword are sold. Furthermore, these placements have different values. In such a setting, SPA is not strategy proof. See Edelman, Ostrovsky, Schwarz. $\endgroup$ – Giskard Feb 23 at 8:36

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